Differential Calculus and Holomorphy: Real and Complex Analysis in Locally Convex Spaces (Mathematics Studies) - ISBN:0444863974

Differential Calculus and Holomorphy: Real and Complex Analysis in Locally Convex Spaces (Mathematics Studies)

Date: 23 May 2011, 15:35

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This book presents the Theory of Differential Calculus and Holomorphy in its modern setting of infinite dimensional (locally convex) spaces. Although this subject has very old roots stemming back to the last century, it has grown very rapidly in the recent years, and most of the results included in this book were available up to now only in article form and, therefore, not really accessible to the non specialist. Furthermore one may reasonnably believe that the general aspect of the Theory will certainly not change fundamentally in the future. Several books on Differential Calculus or on Holomorphy in locally convex spaces already exist, but they do not contain most of the results presented here, which nevertheless have a fundamental character in the Theory.
The reader is only required to have an elementary knowledge of finite dimensional Differential Calculus and Holomorphy, of General Topology, and some familiarity with Hilbert spaces, normed spaces and locally convex spaces at the usual level of a graduate student in Mathematics.

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